GCF of 459/75, 105/565
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 459/75, 105/565 i.e 3/8475 easily. The following is the detailed procedure to determine the greatest common factor of fractions 459/75, 105/565.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 459/75,105/565?
Given fractions are 459/75,105/565
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 459/75,105/565, numerators are 459,105
Denominators are 75,565
The GCF of 459,105 is 3 .
LCM of 75,565 is 8475.
The greatest common factor of 459/75,105/565 = [GCF of 459,105]/[LCM of 75,565]= 3/8475
Therefore, the GCF of 459/75,105/565 is 3/8475.
To find the highest common factor of 459,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 459,105 is 3.
Lets's calculate GCF of 459,105
| 3 | 459, 105 |
| 153, 35 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 459,105 By Matching Biggest Common Factor Method
Now, list down the factors of 459
:1,3,9,17,27,51,153,459
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 459,105 . The biggest common factor number is the GCF number.
So the greatest common factor 459,105 is 3.
Lets's calculate LCM of 75,565
| 5 | 75, 565 |
| 15, 113 |
∴ So the LCM of the given numbers is 5 x 15 x 113 = 8475
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/8475
Therefore, the GCF of Fractions 459/75,105/565 is 3/8475
Least Common Multiple of 75,565 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 75,565 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,565) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(75,565) x common factors =5 x 1 = 5
LCM(75,565) = ( 75 × 565 ) / 5
LCM(75,565) = 42375 / 5
LCM(75,565) = 8475
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 459/75, 105/565
1. What is the HCF of 459,105?
The HCF of 459,105 is 3
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 459/75, 105/565?
Answer: GCF of Numerators as per given numbers 459/75, 105/565 is
GCF of Numerators i.e. for 459,105 is 3
LCM of denominators i.e. for 75,565 is 8475.
Thus, GCF of Fractions is 3/8475.Finally, GCF of Fractions for 459/75, 105/565 is 3/8475.